When an object, such as a rock, is floating in open space it can be moved with minimal effort. This condition is known as "weightlessness" because the object is moved so easily in comparision with the effort that would be required if it were on the surface of the earth and thus had weight. The weight of any object is variable, unlike it's mass which is fixed.
The weight of an object is actually defined by the force of gravity upon it's mass. As long as atoms are in contact, there is no such thing as absolute weightlessness. Weight is the manifestation of the unsuccessful seeking of a zero energy condition of matter.
Gravity is prevented from placing matter as it would like by the electron repulsion of atoms in contact. The like charges of negatively-charged electrons in the atoms prevent gravity from moving them any closer. However, in an object in space subject to no significant exterior gravitational attractions, the internal gravity from all directions will balance out and produce a net weight of zero. In other words weightlessness, or more properly net weightlessness.
But what about the earth? Doesn't our planet fit the definition of a weightless object in space? The earth might have ten trillion times the mass of our rock in space but ten trillion multiplied by a weight of zero is still zero. The gravitational forces toward the center of the earth certainly balance out. This enables the gravity of the moon to strengthen earth's magnetic field as I described in "The Moon And Earth's Magnetic Field" on this blog.
The earth is within the sun's gravitational field but this is expressed in a perpendicular direction by the earth's orbit around the sun. So if the earth as a whole must be weightless, why can't we push it and move it? Maybe we could push it further from the sun to solve global warming.
The trouble is that inward forces within a gravitational system cannot move the system even though it may be weightless as a whole. If we push on the earth with a pole, we are part of the same gravitational system as the earth. The earth pushes back on the pole and the net force is zero. The earth does not move.
Likewise, an object falling in earth's gravity cannot exert a force on the earth as weightless because it becomes a part of the same gravitational system. The falling object does exert a force on the earth but if it is being pulled to earth by gravity, it becomes part of the same gravitational system. However, it is true that the earth and the falling object do combine their momentum.
If we could push against an outside body against the earth, it could conceivably be moved in it's orbit but then we have to consider that the body we would be pushing against would have a mass of it's own and this mass would exert a gravitational force on the earth so that the earth would no longer be weightless. The earth's mass would also exert a gravitational force on the outside body, giving it weight so that we could push against it in our effort to move the earth but this would also give the earth's weight, negating our efforts to move it as a weightless object.
Even though the earth is a weightless object in space, except for the direction of it's orbit around the sun due to the sun's gravity, it could only be moved by a pole of some kind pushing it from an external body such as the moon or a planet, which would also be moved by the effort in proportion to it's mass relative to that of the earth. It could also be moved by an object fired into space from earth, as long as the object exerted a force on the ground and was not a rocket, which is a self-contained gravitational unit. But then, the ratio of the object's mass to the earth's mass would determine how much the earth would move.
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